import geopandas as gpd
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np

pd.set_option('display.max_columns', 500)

import geopandas as gpd

Lab 4: Fire Service Coverage Analysis - Maximal Covering Location Problem

For this lab we return to Fire Service Coverage seeking to assess tradeoffs in service against costs of maintaining different levels of stations.
Instead of covering all demand, the modeling approach tries to maximize the demand covered.
Specifically, we will employ the maximal covering location problem.
Instead of minimizing the number of facilities needed in a previous lab, we now introduce a parameter, $p$, representing a fixed number of facilities to keep in the system.

In Lab 4, there are three research questions we want to look into.

1. Does a change in demand representation impact the optimization results?
2. How can a service system be evaluated to prioritize demand maximization?
3. Can the analysis process be generalized in order to replicate the approach using different demand representations?

The coverage standard for this lab will be fixed at 8000m.

S = 8000

Step 1. Prepare your dataset

Task: Load the three datasets and convert blocks and stations crs into the same one as FDs.crs.

• It is because FDs is in a crs using meter as linear unit.

# Note: it might take time, as FD is a huge file.

FDs = gpd.read_file("Data/California_Fire_Districts.shp")  # load a shapefile containing California Fire District here
blocks = gpd.read_file('Data/sbBlocks_pop.shp')
stations = gpd.read_file("Data/Fire_Stations_SBC.shp") # Load a shapefile containing Fire Stations in Santa Barbara County here

Task: Look into the following Fire District maps.

There are many Fire Districts in California.
We are only going to focus in the "Santa Barbara County Fire District".
In the second map, note that there are many other Fire Districts in Santa Barbara County.
Though it's not shown on the map, they have some overlapping area, which means the area is co-operated by multiple Fire Districts.

FDs.plot("Name")

<Axes: >

blocks = blocks.to_crs(FDs.crs)
stations = stations.to_crs(FDs.crs)

Question 1: Sort out a Fire District out of FDs GeoDataFrame. The district must have its 'Name" column value, "SANTA BARBARA CFD". ( 1 pt )

location_name = "SANTA BARBARA CFD"
SBC_FD = FDs.query("Name == @location_name")

SBC_FD

	OBJECTID	County	FDID	MACSID	Name	Address	City	Zip	FireChief	Phone	Notes	LastUpdate	Website	CALFIREUni	SHAPE_Leng	SHAPE_Area	geometry
223	318	SANTA BARBARA	42035	SBC	SANTA BARBARA CFD	4410 CATHEDRAL OAKS RD	SANTA BARBARA	93110	MARK A. HARTWIG	(805) 681‐5500	None	2018-06-21	https://www.sbcfire.com/	SBC	778360.396807	3.666998e+09	MULTIPOLYGON (((23728.804 -401033.857, 23715.3...

FDs = FDs.loc[FDs.intersects(blocks.unary_union)].reset_index(drop=True)
FDs.plot("Name", legend=True, figsize=(10,10))

<Axes: >

Task: Run following cell, "del FDs". Note: It will delete FDs variable.

We do this because FDs contains a large shapefile, which might burden your RAM.

del FDs

Task: take a subset of stations, within SBC_FD.

NOTE: don't forget to RESET_INDEX() whenever you take a subset!

#set crs to fix problems
stations = stations.to_crs(SBC_FD.crs)
#overlay operation
stations_in_SBC_FD = gpd.sjoin(stations, SBC_FD, predicate='within')
# check result
len(stations_in_SBC_FD)
#rename variables
stations = stations_in_SBC_FD

#reset index
stations.reset_index(drop=True, inplace=True)

stations.plot()

<Axes: >

Question 2: Plot the blocks GeoDataFrame. ( 2 pts )

• Firstly, update the blocks GeoDataFrame's geometry column to have block centroids, not block polygons ( 0.5 pt )
• Secondly, take a subset of blocks which is within the SBC_FD area ( 0.5 pt )
• Thirdly, plot blocks GeoDataFrame with "Population" column. ( 1 pt )
  • figsize=(10,10)
  • opacity must be 0.4
  • take a cmap (colormap) that you like from this webpage (https://matplotlib.org/stable/users/explain/colors/colormaps.html).
  • markersize must be proportional to the column, "Population"
  • ensure you have legend
  • Plot with stations GeoDataFrame

Hint: when there's something you don't know about plot function, refer to this document page (https://geopandas.org/en/stable/docs/reference/api/geopandas.GeoDataFrame.plot.html)! Also, you can Google or ask chatGPT :)

blocks = gpd.read_file('Data/sbBlocks_pop.shp')

#set the crs to the same as the one we will merge with it
blocks = blocks.to_crs('EPSG:3310')
#find the centroid of the blocks 
blocks.geometry = blocks.centroid

blocks

	STATEFP20	COUNTYFP20	TRACTCE20	BLOCKCE20	GEOID20	NAME20	GEOID	Population	F1_Race	White	Black	AmIndian	Asian	Hawaiian	Other	F2__Races	F2_Races	F3_Races	Hispanic_O	Not_Hispan	NH_1_Race	NH_2__Race	NH_2_Races	F18__Popul	F18__1_Rac	F18__Wht	F18__Blk	F18__Ind	F18__Asn	F18__Hwn	F18__Oth	F18__2__Ra	F18__2_Rac	H18__Pop	NH18__Pop	Housing_Un	HU_Occupie	HU_Vacant	Populati_1	GQ_Institu	GQ_Inst_CF	GQ_Inst_Ju	GQ_Inst_Nu	GQ_Inst_Ot	GQ_NonInst	GQ_NonIn_1	GQ_NonIn_2	GQ_NonIn_3	Shape_Leng	Shape_Area	geometry
0	06	083	980500	1005	060839805001005	Block 1005	7500000US060839805001005	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.352988	1.526844e-03	POINT (-55678.105 -354690.532)
1	06	083	002503	1084	060830025031084	Block 1084	7500000US060830025031084	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.171389	4.399815e-05	POINT (-60362.676 -345591.399)
2	06	083	002503	1083	060830025031083	Block 1083	7500000US060830025031083	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.163512	4.814798e-04	POINT (-59882.601 -345033.782)
3	06	083	002503	1085	060830025031085	Block 1085	7500000US060830025031085	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.023011	1.348363e-06	POINT (-60245.991 -345988.216)
4	06	083	002011	1030	060830020111030	Block 1030	7500000US060830020111030	123	109	77	1	1	1	1	28	14	13	1	75	48	47	1	1	77	68	46	1	0	1	0	20	9	8	44	33	39	39	0	0	0	0	0	0	0	0	0	0	0	0.012680	1.411774e-06	POINT (-39831.869 -345910.377)
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
7253	06	083	990000	0032	060839900000032	Block 0032	None	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.845198	4.954950e-03	POINT (26352.947 -449832.111)
7254	06	083	980100	1030	060839801001030	Block 1030	None	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.002871	1.494979e-07	POINT (-1097.203 -453307.679)
7255	06	083	980100	1025	060839801001025	Block 1025	None	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.000896	4.440147e-08	POINT (-42467.263 -442826.614)
7256	06	083	980100	1035	060839801001035	Block 1035	None	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.001724	6.329617e-08	POINT (-7117.185 -443038.484)
7257	06	083	980100	1006	060839801001006	Block 1006	None	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.000707	3.337052e-08	POINT (26585.112 -450096.991)

7258 rows × 51 columns

SBC_FD

	OBJECTID	County	FDID	MACSID	Name	Address	City	Zip	FireChief	Phone	Notes	LastUpdate	Website	CALFIREUni	SHAPE_Leng	SHAPE_Area	geometry
223	318	SANTA BARBARA	42035	SBC	SANTA BARBARA CFD	4410 CATHEDRAL OAKS RD	SANTA BARBARA	93110	MARK A. HARTWIG	(805) 681‐5500	None	2018-06-21	https://www.sbcfire.com/	SBC	778360.396807	3.666998e+09	MULTIPOLYGON (((23728.804 -401033.857, 23715.3...

SBC_FD.geometry[223]

# make a boundary for the area that is covered by the fire stations in a geometry 
#however SBC_FD.geometry still contains the index (1,2,3,4...) so you need to select the entry number 223
blocks.within(SBC_FD.geometry[223])

0        True
1        True
2        True
3       False
4        True
        ...  
7253    False
7254    False
7255    False
7256    False
7257    False
Length: 7258, dtype: bool

# do the overlay using the .loc funciton.inputing the whole geometry that was just found
blocks = blocks.loc[blocks.within(SBC_FD.geometry[223])].reset_index(drop=True)

blocks.plot()

<Axes: >

fig, ax = plt.subplots(figsize=(10,10))
opacity = .4

marker_size = blocks['Population']*1


blocks.plot(column='Population', cmap="hsv", ax=ax,legend=True, legend_kwds={'label': 'Population'})
plt.xlabel('Longitude')
plt.ylabel('Latitude')
plt.title('Population of Blocks')

sc = ax.scatter(blocks.geometry.x, blocks.geometry.y, s=marker_size, alpha=opacity, c=blocks["Population"])

legend = ax.legend(*sc.legend_elements(), title="Population", loc='lower right')
ax.add_artist(legend)

plt.show()

Step 2. Conduct MCLP

Decision Variables: \begin{align*} & x_j = \begin{cases} 1, & \text{if facility $j$ is open}, \\ 0, & \text{otherwise}. \end{cases} \\ & y_i = \begin{cases} 1, & \text{if demand $i$ is covered}, \\ 0, & \text{otherwise}. \end{cases} \end{align*}

Parameters: \begin{align*} & I = \text{number of demands}, \\ & J = \text{number of facilities}, \\ & S = \text{Coverage Distance Standard}, \\ & a_i = \text{Weight assigned to demand $i$}, \\ & D_{ij} = \text{Distance between demand $i$ and facility $j$}, \\ & N_i = \{ j \in J \, | \, D_{ij} \leq S \}, \\ & P = \text{the number of facilities to be opened}. \end{align*}

Objective Function: \begin{align*} \text{Maximize:} \quad & \sum_{i=1}^{I} a_i y_i \end{align*}

Constraints: \begin{align*} \text{Subject to:} \quad & \sum_{j \in N_i} x_j \geq y_i, \quad \forall i \in I \\ & \sum_{j=1}^{J} x_j \leq P, \\ & x_j, y_i \in \{0, 1\}, \quad \forall i, j. \end{align*}

Task: Based on the mathematical Model, set the I and J values correctly.

• In this section, we will consider each block as demand $i$
• we will consider each existing fire station as facility $j$
• In the beginning of this lab, we defined our S value to be 8000 meter, 8 km.
• Pick any P that is less than current number of stations :)

I =len(blocks)
J = len(stations_in_SBC_FD)
P =26

Task: We are going to have block's population as weight assigned to demand. Define $a_i$.

a_i = blocks['Population']

Task: Create $D_{ij}$ variable using Euclidean Distance between demand $i$ and facility $j$.

distances = blocks.geometry.apply(lambda geom: stations_in_SBC_FD.distance(geom))
D_ij = distances.to_numpy()

D_ij

array([[10488.6795986 , 11964.87591378, 23611.82413809, ...,
        66741.68258625, 53218.36841912, 20151.87176686],
       [20682.54861226, 22152.31938929, 33461.47908875, ...,
        75109.10054863, 61787.71166349, 30028.9029038 ],
       [21011.56653512, 22390.74572891, 33890.975921  , ...,
        74974.6012877 , 61684.30027088, 30161.1291684 ],
       ...,
       [70568.5385688 , 67755.61573941, 65491.09933567, ...,
        15539.22357526, 26434.05002471, 59030.5035491 ],
       [18211.13870167, 19262.59329051,  5978.1092757 , ...,
        61272.96507486, 48520.81899437, 20396.47029567],
       [72889.29787724, 70070.13567839, 67820.57571675, ...,
        17199.2022653 , 28577.3517051 , 61344.79287098]])

Question 3: Create $N_i$ variable in list format. ( 1 pt )

• Previously, $N_i$ in dictionary is introduced.
• With your understanding so far, list format of $N_i$ can also be created.
• You can use double for-loops, or list comprehension.

# This is a hint for students who want to do it with list comprehension


# Creating a two-dimensional list
matrix = [[1, 2, 3],
          [4, 5, 6],
          [7, 8, 9],
          [10, 11, 12]]

# Using list comprehension to filter even numbers from the matrix
# The '%' symbol in Python is called the modulo operator. 
    #It returns the remainder of the division of the left operand by the right operand.
even_numbers = [[matrix[r][c] for c in range(len(matrix[0])) if matrix[r][c]%2 == 0]
                for r in range(len(matrix))]

print(even_numbers)

[[2], [4, 6], [8], [10, 12]]

S

8000

N_i = {i: [j for j in range(J) if D_ij[i][j] <= S] for i in range(I)}
len(N_i)

3224

Question 4: Complete the Optimization Model ( 6 pts )

import gurobipy as gp
from gurobipy import GRB
# Create a new Gurobi model
mclp = gp.Model("Maximal_Covering_Location")

# Decision Variables
x = mclp.addVars(J, vtype = GRB.BINARY, name ="x") #if the facility covered or not
y = mclp.addVars(I, vtype=GRB.BINARY, name ="y") #if the demand is covered or not

# Objective Function
mclp.setObjective(gp.quicksum(y[i]*a_i[i] for i in range(I)), GRB.MAXIMIZE) #maximise the demand covered with the facilities avalable

# Constraints
# Each demand must be covered by neighboring facility or it will just take all of the stations
for i in range(I):
    mclp.addConstr(gp.quicksum(x[j] for j in N_i[i]) >= y[i])

# Number of opened facilities must not exceed P
mclp.addConstr(gp.quicksum(x[j] for j in range(J)) <= P)

# Optimize the model
mclp.optimize()

Set parameter TokenServer to value "gurobi.geog.ucsb.edu"
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xba252813
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%

Question 5: Take a subset of stations based on the model output. ( 1 pt )

open_stations_index = [j for j in range(J) if x[j].X > 0.5]
print(f"Open stations: {open_stations_index}")
print(f"Number of open stations: {len(open_stations_index)}")

Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 25, 26]
Number of open stations: 19

# open_stations = gpd.GeoDataFrame(geometry=[stations_in_SBC_FD for j in open_stations_index])
open_stations = stations_in_SBC_FD.iloc[open_stations_index]

Question 6: Plot the open_stations and their coverage buffers with the demand buffers. ( 2 pts )

• Copy and Paste the plotting code from Question 2.
• Replace stations with open_stations.
• Add another plot function which plots the buffer with buffer distance S from each open_station.
  • The coverage buffer shouldn't have facecolor
  • Buffer Boundary must be dashed lines. (ask chatGPT of google how to do this!)

A = blocks.plot("Population", figsize = (10,10), alpha = .4, cmap = 'gnuplot', markersize = blocks["Population"], legend = True,
               legend_kwds={'label': "Population"})
                            
open_stations.plot(ax=A, label="open_stations", color = "blue")
buffer = open_stations.buffer(S)
buffer.plot(ax=A, linestyle="--", facecolor='none')

<Axes: >

open_stations.plot

<geopandas.plotting.GeoplotAccessor object at 0x000002BD517A5B40>

Step 3. Functionize / Modularize

Here, we will functionize our optimization model.
So that with given P value, the model can be solved.

Question 7: Functionize your code out of Question 4 and 5 ( 2 pts )

• start defining a function named, "solve_mclp". ( 0.5 pts )
• The function takes one argument, P. ( 0.5 pts )
• Within the function, copy and paste the code you did for Question 4 and 5. ( 0.5 pts )
• Then, add the last line of code, to return open_stations, and mclp.obj_val ( 0.5 pts )

# Let me give you functionize example.
# For more, refer to Lab 0.

sample_list = [1,2,3,4]

def sum_array(a):
    s = 0
    a = np.array(a)
    for num in a:
        s += num
    return s, a # Return the summation of all elements, and the original array

sum_array(sample_list)

(10, array([1, 2, 3, 4]))

def solve_mclp(P):
    #question 4
    mclp = gp.Model("Maximal_Covering_Location")

# Decision Variables
    x = mclp.addVars(J, vtype = GRB.BINARY, name ="x") #if the facility covered or not
    y = mclp.addVars(I, vtype=GRB.BINARY, name ="y") #if the demand is covered or not

# Objective Function
    mclp.setObjective(gp.quicksum(y[i]*a_i[i] for i in range(I)), GRB.MAXIMIZE) #maximise the demand covered with the facilities avalable

# Constraints
# Each demand must be covered by neighboring facility or it will just take all of the stations
    for i in range(I):
        mclp.addConstr(gp.quicksum(x[j] for j in N_i[i]) >= y[i])

# Number of opened facilities must not exceed P
    mclp.addConstr(gp.quicksum(x[j] for j in range(J)) <= P)

# Optimize the model
    mclp.optimize()

#question 5   
    open_stations_index = [j for j in range(J) if x[j].X > 0.5]
    print(f"Open stations: {open_stations_index}")
    print(f"Number of open stations: {len(open_stations_index)}")
    open_stations = stations_in_SBC_FD.iloc[open_stations_index]
    

    return open_stations, mclp.obj_val

Step 4. Evaluate the Result

Question 8: To evaluate the optimization result, we always compare with the current operation. Calculate current_coverage. ( 2 pts )

Current coverage is the sum of all the demand weights, currently covered by existing stations.
Here are the thought process you can go through.

• Create buffers with distance S out of all the existing stations.
• Take a unary_union of the buffers. ( 0.5 pts )
• Use .within() function to take a subset of blocks, within the unary_union of coverage buffers. ( 0.5 pts )
• Take the Population column out of the subset of blocks. ( 0.5 pts )
• Take the sum of the column values. ( 0.5 pts )

current = stations.buffer(S).unary_union

coverage = blocks.loc[blocks.within(current)].reset_index(drop=True)
coverage = coverage["Population"].sum()
coverage

167606

Task: Check if provided code works with your defined function, solve_mclp

selecteds = []  # List to store selected stations for each value of p
obj_vals = []   # List to store objective values for each value of p

# Iterate over values of p starting from 3
for p in range(3, len(stations)+1):
    print(f"=================== for P={p}")  # Print current value of p
    # Call solve_mclp function to solve the problem for current value of p
    selected_stations, obj_val = solve_mclp(p)
    # Append selected stations to the selecteds list
    selecteds.append(selected_stations)
    # Append objective value to the obj_vals list
    obj_vals.append(obj_val)

=================== for P=3
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xc1148ef3
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+00, 3e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 28463.000000

Root relaxation: objective 1.420460e+05, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    142046.00000 142046.000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 142046 28463 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.420460000000e+05, best bound 1.420460000000e+05, gap 0.0000%
Open stations: [5, 16, 19]
Number of open stations: 3
=================== for P=4
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xd9224489
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e+00, 4e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 35944.000000

Root relaxation: objective 1.535990e+05, 20 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    153599.00000 153599.000  0.00%     -    0s

Explored 1 nodes (20 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 153599 35944 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.535990000000e+05, best bound 1.535990000000e+05, gap 0.0000%
Open stations: [5, 16, 17, 19]
Number of open stations: 4
=================== for P=5
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x1e8621a4
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e+00, 5e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 101213.00000

Root relaxation: objective 1.578710e+05, 19 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    157871.00000 157871.000  0.00%     -    0s

Explored 1 nodes (19 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 157871 101213 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.578710000000e+05, best bound 1.578710000000e+05, gap 0.0000%
Open stations: [5, 9, 16, 17, 22]
Number of open stations: 5
=================== for P=6
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x4872ed6f
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [6e+00, 6e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 103347.00000

Root relaxation: objective 1.615640e+05, 16 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    161564.00000 161564.000  0.00%     -    0s

Explored 1 nodes (16 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 161564 103347 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.615640000000e+05, best bound 1.615640000000e+05, gap 0.0000%
Open stations: [5, 9, 16, 17, 18, 22]
Number of open stations: 6
=================== for P=7
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x50c869a2
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [7e+00, 7e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 138503.00000

Root relaxation: objective 1.636980e+05, 14 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    163698.00000 163698.000  0.00%     -    0s

Explored 1 nodes (14 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 163698 138503 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.636980000000e+05, best bound 1.636980000000e+05, gap 0.0000%
Open stations: [5, 9, 14, 16, 17, 18, 22]
Number of open stations: 7
=================== for P=8
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xc631c009
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [8e+00, 8e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 139069.00000

Root relaxation: objective 1.656950e+05, 11 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    165695.00000 165695.000  0.00%     -    0s

Explored 1 nodes (11 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 165695 139069 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.656950000000e+05, best bound 1.656950000000e+05, gap 0.0000%
Open stations: [4, 9, 14, 16, 17, 18, 22, 26]
Number of open stations: 8
=================== for P=9
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xde1bae41
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [9e+00, 9e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 139439.00000

Root relaxation: objective 1.663330e+05, 11 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    166333.00000 166333.000  0.00%     -    0s

Explored 1 nodes (11 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 166333 139439 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.663330000000e+05, best bound 1.663330000000e+05, gap 0.0000%
Open stations: [4, 9, 11, 14, 16, 17, 18, 22, 26]
Number of open stations: 9
=================== for P=10
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xda05e924
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 139558.00000

Root relaxation: objective 1.668990e+05, 6 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    166899.00000 166899.000  0.00%     -    0s

Explored 1 nodes (6 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 166899 139558 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.668990000000e+05, best bound 1.668990000000e+05, gap 0.0000%
Open stations: [4, 9, 11, 13, 14, 16, 17, 18, 22, 26]
Number of open stations: 10
=================== for P=11
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x4f3e9f77
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 140196.00000

Root relaxation: objective 1.671390e+05, 6 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167139.00000 167139.000  0.00%     -    0s

Explored 1 nodes (6 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 167139 140196 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.671390000000e+05, best bound 1.671390000000e+05, gap 0.0000%
Open stations: [4, 6, 9, 11, 13, 14, 16, 17, 18, 22, 26]
Number of open stations: 11
=================== for P=12
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x1e3b83ba
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 140425.00000

Root relaxation: objective 1.673330e+05, 3 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167333.00000 167333.000  0.00%     -    0s

Explored 1 nodes (3 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 167333 140425 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.673330000000e+05, best bound 1.673330000000e+05, gap 0.0000%
Open stations: [2, 4, 6, 9, 11, 13, 14, 16, 17, 18, 22, 26]
Number of open stations: 12
=================== for P=13
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x209b8da2
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167360.00000

Root relaxation: objective 1.674520e+05, 2 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167452.00000 167452.000  0.00%     -    0s

Explored 1 nodes (2 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 167452 167360 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.674520000000e+05, best bound 1.674520000000e+05, gap 0.0000%
Open stations: [2, 4, 6, 9, 11, 13, 14, 16, 17, 18, 22, 23, 26]
Number of open stations: 13
=================== for P=14
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x03cf73b5
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167374.00000

Root relaxation: objective 1.675220e+05, 2 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167522.00000 167522.000  0.00%     -    0s

Explored 1 nodes (2 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 167522 167374 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.675220000000e+05, best bound 1.675220000000e+05, gap 0.0000%
Open stations: [2, 4, 6, 9, 11, 13, 14, 16, 17, 18, 22, 23, 25, 26]
Number of open stations: 14
=================== for P=15
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x952e5b76
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167443.00000

Root relaxation: objective 1.675910e+05, 1 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167591.00000 167591.000  0.00%     -    0s

Explored 1 nodes (1 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 167591 167443 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.675910000000e+05, best bound 1.675910000000e+05, gap 0.0000%
Open stations: [2, 4, 6, 9, 11, 12, 13, 14, 16, 17, 18, 22, 23, 25, 26]
Number of open stations: 15
=================== for P=16
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xcd3e3dcd
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167605.00000

Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 2: 167605 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676050000000e+05, best bound 1.676050000000e+05, gap 0.0000%
Open stations: [2, 4, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 22, 23, 25, 26]
Number of open stations: 16
=================== for P=17
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x0e5accf5
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3203 rows and 3211 columns
Presolve time: 0.01s
Presolved: 22 rows, 41 columns, 90 nonzeros
Found heuristic solution: objective 167606.00000
Variable types: 0 continuous, 41 integer (41 binary)

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
Open stations: [1, 2, 4, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 22, 23, 25, 26]
Number of open stations: 17
=================== for P=18
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xbd53d068
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3210 rows and 3218 columns
Presolve time: 0.00s
Presolved: 15 rows, 34 columns, 62 nonzeros
Found heuristic solution: objective 167606.00000
Variable types: 0 continuous, 34 integer (34 binary)

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
Open stations: [1, 2, 4, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 22, 23, 25, 26]
Number of open stations: 17
=================== for P=19
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x4d9615ea
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
Open stations: [1, 2, 4, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 25, 26]
Number of open stations: 18
=================== for P=20
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x06e3d55a
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 25, 26]
Number of open stations: 19
=================== for P=21
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xac9379a7
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 25, 26]
Number of open stations: 19
=================== for P=22
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x294b1219
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 25, 26]
Number of open stations: 19
=================== for P=23
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x9b75ffee
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 25, 26]
Number of open stations: 19
=================== for P=24
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x4030e886
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 25, 26]
Number of open stations: 19
=================== for P=25
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x80c372e9
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 25, 26]
Number of open stations: 19
=================== for P=26
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xba252813
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 25, 26]
Number of open stations: 19
=================== for P=27
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xb06b9a49
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 22, 23, 24, 25, 26]
Number of open stations: 19
=================== for P=28
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xe144439c
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
Open stations: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]
Number of open stations: 28

Task: Check if the output Table is plausible. And learn how to create a pandas DataFrame

• To create a DataFrame, you can call pandas.DataFrame() and deliver a dictionary.
• The dictionary will have key and value pairs.
  • key will be the column name
  • value will be an array of column values

results = pd.DataFrame({
    'P': range(3, len(stations)+1),
    'Coverage': obj_vals
})
results

	P	Coverage
0	3	142046.0
1	4	153599.0
2	5	157871.0
3	6	161564.0
4	7	163698.0
5	8	165695.0
6	9	166333.0
7	10	166899.0
8	11	167139.0
9	12	167333.0
10	13	167452.0
11	14	167522.0
12	15	167591.0
13	16	167605.0
14	17	167606.0
15	18	167606.0
16	19	167606.0
17	20	167606.0
18	21	167606.0
19	22	167606.0
20	23	167606.0
21	24	167606.0
22	25	167606.0
23	26	167606.0
24	27	167606.0
25	28	167606.0

def scatterplot_result(results):
    # Plot the DataFrame, in scatter plot, taking P values as x and Coverage values as y
    results.plot(kind="scatter", x="P", y="Coverage")
    # Add grid lines
    plt.grid(True)
    # Add the current coverage point in color red
    plt.scatter(len(stations), coverage, color="red")
    # provide a dashed red line to inform current coverage
    plt.axhline(y=coverage, color='r', linestyle='--', label='Current Coverage')
    # show the plot!
    plt.show()
    
scatterplot_result(results)

Task: Put your code to plot open_stations and coverage buffer from Question 6.

Feel free to edit any other plotting details

def map_result(p, demand_block=True):
    open_stations = selecteds[p-3]
    
    fig, ax = plt.subplots(figsize=(10, 10))


    blocks.plot(column="Population", 
                ax=ax,
                alpha=0.4, 
                cmap='gnuplot',
                markersize=blocks["Population"],
                legend=False  # No legend here
    )


    open_stations.plot(ax=ax, label="Open Stations", color="red", markersize=50)
    
    # buffer 
    buffer = open_stations.buffer(S)
    buffer.plot(ax=ax, linestyle="--", edgecolor='blue', facecolor='none')

    if demand_block:
        blocks.plot(column="Population", ax=ax, markersize=5, alpha=0.4, legend=True, cmap='gnuplot')
    else:
        fishnet_points.plot(ax=ax, color='green', markersize=5)
        
    handles, labels = ax.get_legend_handles_labels()
    ax.legend(handles, labels, title='Legend')

    plt.title(f"{p} stations open")
    plt.show()
    
map_result(13) # Try different p!

Task: Following function is to go through the whole process. Check if you get the same output as before :)

def optimize_and_evaluate(demand_block=True):
    selecteds = [] 
    obj_vals = [] 
    for p in range(3, len(stations)+1):
        print(f"=================== for P={p}")
        selected_stations, obj_val = solve_mclp(p)
        selecteds.append(selected_stations)
        obj_vals.append(obj_val)
        map_result(p, demand_block)
        
    results = pd.DataFrame({
        'P': range(3, len(stations)+1),
        'Coverage': obj_vals
    })
    scatterplot_result(results)

optimize_and_evaluate()

=================== for P=3
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xc1148ef3
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+00, 3e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 28463.000000

Root relaxation: objective 1.420460e+05, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    142046.00000 142046.000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 142046 28463 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.420460000000e+05, best bound 1.420460000000e+05, gap 0.0000%
Open stations: [5, 16, 19]
Number of open stations: 3

=================== for P=4
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xd9224489
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e+00, 4e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 35944.000000

Root relaxation: objective 1.535990e+05, 20 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    153599.00000 153599.000  0.00%     -    0s

Explored 1 nodes (20 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 153599 35944 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.535990000000e+05, best bound 1.535990000000e+05, gap 0.0000%
Open stations: [5, 16, 17, 19]
Number of open stations: 4

=================== for P=5
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x1e8621a4
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e+00, 5e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 101213.00000

Root relaxation: objective 1.578710e+05, 19 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    157871.00000 157871.000  0.00%     -    0s

Explored 1 nodes (19 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 157871 101213 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.578710000000e+05, best bound 1.578710000000e+05, gap 0.0000%
Open stations: [5, 9, 16, 17, 22]
Number of open stations: 5

=================== for P=6
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x4872ed6f
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [6e+00, 6e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 103347.00000

Root relaxation: objective 1.615640e+05, 16 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    161564.00000 161564.000  0.00%     -    0s

Explored 1 nodes (16 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 161564 103347 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.615640000000e+05, best bound 1.615640000000e+05, gap 0.0000%
Open stations: [5, 9, 16, 17, 18, 22]
Number of open stations: 6

=================== for P=7
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x50c869a2
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [7e+00, 7e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 138503.00000

Root relaxation: objective 1.636980e+05, 14 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    163698.00000 163698.000  0.00%     -    0s

Explored 1 nodes (14 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 163698 138503 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.636980000000e+05, best bound 1.636980000000e+05, gap 0.0000%
Open stations: [5, 9, 14, 16, 17, 18, 22]
Number of open stations: 7

=================== for P=8
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xc631c009
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [8e+00, 8e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 139069.00000

Root relaxation: objective 1.656950e+05, 11 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    165695.00000 165695.000  0.00%     -    0s

Explored 1 nodes (11 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 165695 139069 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.656950000000e+05, best bound 1.656950000000e+05, gap 0.0000%
Open stations: [4, 9, 14, 16, 17, 18, 22, 26]
Number of open stations: 8

=================== for P=9
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xde1bae41
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [9e+00, 9e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 139439.00000

Root relaxation: objective 1.663330e+05, 11 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    166333.00000 166333.000  0.00%     -    0s

Explored 1 nodes (11 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 166333 139439 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.663330000000e+05, best bound 1.663330000000e+05, gap 0.0000%
Open stations: [4, 9, 11, 14, 16, 17, 18, 22, 26]
Number of open stations: 9

=================== for P=10
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xda05e924
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 139558.00000

Root relaxation: objective 1.668990e+05, 6 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    166899.00000 166899.000  0.00%     -    0s

Explored 1 nodes (6 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 166899 139558 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.668990000000e+05, best bound 1.668990000000e+05, gap 0.0000%
Open stations: [4, 9, 11, 13, 14, 16, 17, 18, 22, 26]
Number of open stations: 10

=================== for P=11
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x4f3e9f77
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 140196.00000

Root relaxation: objective 1.671390e+05, 6 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167139.00000 167139.000  0.00%     -    0s

Explored 1 nodes (6 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 167139 140196 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.671390000000e+05, best bound 1.671390000000e+05, gap 0.0000%
Open stations: [4, 6, 9, 11, 13, 14, 16, 17, 18, 22, 26]
Number of open stations: 11

=================== for P=12
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x1e3b83ba
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 140425.00000

Root relaxation: objective 1.673330e+05, 3 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167333.00000 167333.000  0.00%     -    0s

Explored 1 nodes (3 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 167333 140425 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.673330000000e+05, best bound 1.673330000000e+05, gap 0.0000%
Open stations: [2, 4, 6, 9, 11, 13, 14, 16, 17, 18, 22, 26]
Number of open stations: 12

=================== for P=13
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x209b8da2
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167360.00000

Root relaxation: objective 1.674520e+05, 2 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167452.00000 167452.000  0.00%     -    0s

Explored 1 nodes (2 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 167452 167360 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.674520000000e+05, best bound 1.674520000000e+05, gap 0.0000%
Open stations: [2, 4, 6, 9, 11, 13, 14, 16, 17, 18, 22, 23, 26]
Number of open stations: 13

=================== for P=14
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x03cf73b5
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167374.00000

Root relaxation: objective 1.675220e+05, 2 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167522.00000 167522.000  0.00%     -    0s

Explored 1 nodes (2 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 167522 167374 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.675220000000e+05, best bound 1.675220000000e+05, gap 0.0000%
Open stations: [2, 4, 6, 9, 11, 13, 14, 16, 17, 18, 22, 23, 25, 26]
Number of open stations: 14

=================== for P=15
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x952e5b76
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167443.00000

Root relaxation: objective 1.675910e+05, 1 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    167591.00000 167591.000  0.00%     -    0s

Explored 1 nodes (1 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 167591 167443 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.675910000000e+05, best bound 1.675910000000e+05, gap 0.0000%
Open stations: [2, 4, 6, 9, 11, 12, 13, 14, 16, 17, 18, 22, 23, 25, 26]
Number of open stations: 15

=================== for P=16
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xcd3e3dcd
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 3209 columns
Presolve time: 0.00s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167605.00000

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 2: 167605 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676050000000e+05, best bound 1.676050000000e+05, gap 0.0000%
Open stations: [2, 4, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 22, 23, 25, 26]
Number of open stations: 16

=================== for P=17
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x0e5accf5
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3203 rows and 3211 columns
Presolve time: 0.01s
Presolved: 22 rows, 41 columns, 90 nonzeros
Found heuristic solution: objective 167606.00000
Variable types: 0 continuous, 41 integer (41 binary)

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
Open stations: [1, 2, 4, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 22, 23, 25, 26]
Number of open stations: 17

=================== for P=18
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xbd53d068
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3210 rows and 3218 columns
Presolve time: 0.00s
Presolved: 15 rows, 34 columns, 62 nonzeros
Found heuristic solution: objective 167606.00000
Variable types: 0 continuous, 34 integer (34 binary)

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
Open stations: [1, 2, 4, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 22, 23, 25, 26]
Number of open stations: 17

=================== for P=19
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x4d9615ea
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
Open stations: [1, 2, 4, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 25, 26]
Number of open stations: 18

=================== for P=20
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x06e3d55a
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.02s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 25, 26]
Number of open stations: 19

=================== for P=21
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xac9379a7
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 25, 26]
Number of open stations: 19

=================== for P=22
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x294b1219
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 25, 26]
Number of open stations: 19

=================== for P=23
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x9b75ffee
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 25, 26]
Number of open stations: 19

=================== for P=24
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x4030e886
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 25, 26]
Number of open stations: 19

=================== for P=25
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0x80c372e9
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 25, 26]
Number of open stations: 19

=================== for P=26
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xba252813
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 25, 26]
Number of open stations: 19

=================== for P=27
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xb06b9a49
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 22, 23, 24, 25, 26]
Number of open stations: 19

=================== for P=28
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3225 rows, 3252 columns and 13191 nonzeros
Model fingerprint: 0xe144439c
Variable types: 0 continuous, 3252 integer (3252 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 3e+03]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 3252 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 167606 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
Open stations: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]
Number of open stations: 28

Step 4. Replicate your Analysis with different Demand Representations

Task: Review from Lab 2. We are creating fishnet points within the SBC_FD

boundary = SBC_FD.envelope # .envelope gives you the bounding rectangle of given GeoDataFrame.
boundary.bounds

	minx	miny	maxx	maxy
223	-61331.613	-401270.1778	50847.5684	-323367.7559

minx, miny, maxx, maxy = boundary.loc[223].bounds
print(minx, miny, maxx, maxy)

-61331.61300000176 -401270.1777999997 50847.56839999929 -323367.7559000002

from shapely.geometry import Point

# Here, we are going to create fishnet points.
    # Fishnet points are points spaced with an equal interval.
    # You'll see when you see the output!

# Define the interval between points 
#### Note: Adjust interval value as needed for lab question 2
def create_fishnet(interval):
# Create arrays of x and y coordinates using np.arange
    x_coords = np.arange(minx, maxx, interval)
    y_coords = np.arange(miny, maxy, interval)

    # Create a list to store the points
    fishnet_points = []

    # Generate points for the fishnet
    for y in y_coords:
        for x in x_coords:
            fishnet_points.append((x, y))

    # Print the number of points generated
    print("Number of points in the fishnet:", len(fishnet_points))

    fishnet_points = gpd.GeoSeries([Point(pt_cd) for pt_cd in fishnet_points])
    fishnet_points = fishnet_points[fishnet_points.within(SBC_FD.geometry[223])]
    fishnet_points.plot(figsize=(15,5))
    return fishnet_points

interval = 5280/5  # default: 5280/5 feet (1 mile / 5 = 0.2 mile) 
fishnet_points = create_fishnet(interval)

Number of points in the fishnet: 7918

# Current Coverage
current_coverage = fishnet_points.within(stations.buffer(S).unary_union).sum()
current_coverage

1795

fishnet_points = fishnet_points.reset_index(drop=True)
fishnet_points.geometry
len(fishnet_points)

3304

Question 9: Re-compute the model variables here for fishnet_points, instead of blocks. ( 1 pt )

Note: all the fishnet points will have the same weight, 1.

I = len(fishnet_points)
J =len(stations)
a_i = [1]*I
D_ij = [[np.sqrt((fishnet_points.geometry.x[i] - stations.geometry.x[j])**2 + 
                 (fishnet_points.geometry.y[i] - stations.geometry.y[j])**2)
                  for j in range(J)] for i in range(I)]
N_i = [[j for j in range(J) if D_ij[i][j] <= S] for i in range(I)]

optimize_and_evaluate(demand_block=False)

=================== for P=3
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x3f7c710c
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+00, 3e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 506.0000000

Root relaxation: objective 5.400000e+02, 45 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     540.0000000  540.00000  0.00%     -    0s

Explored 1 nodes (45 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 540 506 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 5.400000000000e+02, best bound 5.400000000000e+02, gap 0.0000%
Open stations: [1, 6, 14]
Number of open stations: 3

=================== for P=4
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xa01cdfc9
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e+00, 4e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 582.0000000

Root relaxation: objective 7.040000e+02, 46 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     704.0000000  704.00000  0.00%     -    0s

Explored 1 nodes (46 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 704 582 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 7.040000000000e+02, best bound 7.040000000000e+02, gap 0.0000%
Open stations: [1, 6, 14, 15]
Number of open stations: 4

=================== for P=5
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xb95f9119
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e+00, 5e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 675.0000000

Root relaxation: objective 8.550000e+02, 43 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0     855.0000000  855.00000  0.00%     -    0s

Explored 1 nodes (43 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 855 675 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 8.550000000000e+02, best bound 8.550000000000e+02, gap 0.0000%
Open stations: [1, 2, 6, 14, 15]
Number of open stations: 5

=================== for P=6
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xdc018ef8
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [6e+00, 6e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 746.0000000

Root relaxation: objective 1.005000e+03, 39 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1005.0000000 1005.00000  0.00%     -    0s

Explored 1 nodes (39 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 1005 746 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.005000000000e+03, best bound 1.005000000000e+03, gap 0.0000%
Open stations: [1, 2, 4, 6, 14, 15]
Number of open stations: 6

=================== for P=7
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xd4eb132b
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [7e+00, 7e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 929.0000000

Root relaxation: objective 1.146000e+03, 38 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1146.0000000 1146.00000  0.00%     -    0s

Explored 1 nodes (38 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 1146 929 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.146000000000e+03, best bound 1.146000000000e+03, gap 0.0000%
Open stations: [2, 4, 6, 14, 15, 17, 18]
Number of open stations: 7

=================== for P=8
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x05e3c257
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [8e+00, 8e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1086.0000000

Root relaxation: objective 1.270000e+03, 30 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1270.0000000 1270.00000  0.00%     -    0s

Explored 1 nodes (30 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 1270 1086 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.270000000000e+03, best bound 1.270000000000e+03, gap 0.0000%
Open stations: [2, 4, 6, 13, 14, 16, 17, 18]
Number of open stations: 8

=================== for P=9
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xf7ea4d1e
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [9e+00, 9e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1177.0000000

Root relaxation: objective 1.384000e+03, 30 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1384.0000000 1384.00000  0.00%     -    0s

Explored 1 nodes (30 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 1384 1177 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.384000000000e+03, best bound 1.384000000000e+03, gap 0.0000%
Open stations: [2, 4, 6, 11, 13, 14, 16, 17, 18]
Number of open stations: 9

=================== for P=10
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x7467d208
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1291.0000000

Root relaxation: objective 1.475000e+03, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1475.0000000 1475.00000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 1475 1291 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.475000000000e+03, best bound 1.475000000000e+03, gap 0.0000%
Open stations: [2, 4, 6, 11, 13, 14, 16, 17, 18, 25]
Number of open stations: 10

=================== for P=11
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x10c3d27f
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1433.0000000

Root relaxation: objective 1.564000e+03, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1564.0000000 1564.00000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 1564 1433 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.564000000000e+03, best bound 1.564000000000e+03, gap 0.0000%
Open stations: [2, 4, 6, 11, 13, 14, 16, 17, 18, 24, 25]
Number of open stations: 11

=================== for P=12
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x649633df
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1493.0000000

Root relaxation: objective 1.647000e+03, 27 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1647.0000000 1647.00000  0.00%     -    0s

Explored 1 nodes (27 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 1647 1493 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.647000000000e+03, best bound 1.647000000000e+03, gap 0.0000%
Open stations: [2, 4, 6, 11, 13, 14, 16, 17, 18, 23, 24, 25]
Number of open stations: 12

=================== for P=13
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x9b95d984
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1591.0000000

Root relaxation: objective 1.715000e+03, 18 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1715.0000000 1715.00000  0.00%     -    0s

Explored 1 nodes (18 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 1715 1591 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.715000000000e+03, best bound 1.715000000000e+03, gap 0.0000%
Open stations: [2, 4, 6, 11, 12, 13, 14, 16, 17, 18, 23, 24, 25]
Number of open stations: 13

=================== for P=14
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xdadf5112
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1611.0000000

Root relaxation: objective 1.743000e+03, 17 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1743.0000000 1743.00000  0.00%     -    0s

Explored 1 nodes (17 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 1743 1611 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.743000000000e+03, best bound 1.743000000000e+03, gap 0.0000%
Open stations: [1, 2, 4, 6, 11, 12, 13, 14, 16, 17, 18, 23, 24, 25]
Number of open stations: 14

=================== for P=15
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xe090a64f
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1646.0000000

Root relaxation: objective 1.763000e+03, 14 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1763.0000000 1763.00000  0.00%     -    0s

Explored 1 nodes (14 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 1763 1646 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.763000000000e+03, best bound 1.763000000000e+03, gap 0.0000%
Open stations: [1, 2, 4, 6, 11, 12, 13, 14, 15, 16, 17, 18, 23, 24, 25]
Number of open stations: 15

=================== for P=16
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xc848a4a7
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1714.0000000

Root relaxation: objective 1.780000e+03, 8 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0    1780.0000000 1780.00000  0.00%     -    0s

Explored 1 nodes (8 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 1780 1714 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.780000000000e+03, best bound 1.780000000000e+03, gap 0.0000%
Open stations: [1, 2, 4, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 22, 23, 25]
Number of open stations: 16

=================== for P=17
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x743280a7
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1789.0000000

Root relaxation: cutoff, 3 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0     cutoff    0      1789.00000 1789.00000  0.00%     -    0s

Explored 1 nodes (3 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 2: 1789 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.789000000000e+03, best bound 1.789000000000e+03, gap 0.0000%
Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 22, 23, 25]
Number of open stations: 17

=================== for P=18
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xbb43ee56
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1793.0000000

Root relaxation: infeasible, 1 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0 infeasible    0      1793.00000 1793.00000  0.00%     -    0s

Explored 1 nodes (1 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 2: 1793 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.793000000000e+03, best bound 1.793000000000e+03, gap 0.0000%
Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 22, 23, 25, 26]
Number of open stations: 18

=================== for P=19
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xa9cc7751
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 3263 columns
Presolve time: 0.00s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1797.0000000

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 22, 23, 25, 26, 27]
Number of open stations: 19

=================== for P=20
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x3c5cc094
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3261 rows and 3264 columns
Presolve time: 0.01s
Presolved: 44 rows, 68 columns, 192 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 68 integer (68 binary)

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 22, 23, 25, 26, 27]
Number of open stations: 19

=================== for P=21
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xa72ab122
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3264 rows and 3267 columns
Presolve time: 0.01s
Presolved: 41 rows, 65 columns, 174 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 65 integer (65 binary)

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 22, 23, 25, 26, 27]
Number of open stations: 19

=================== for P=22
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xf698ea55
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3272 rows and 3275 columns
Presolve time: 0.01s
Presolved: 33 rows, 57 columns, 134 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 57 integer (57 binary)

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 22, 23, 25, 26, 27]
Number of open stations: 19

=================== for P=23
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xf679243a
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3285 rows and 3288 columns
Presolve time: 0.00s
Presolved: 20 rows, 44 columns, 82 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 44 integer (44 binary)

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
Open stations: [0, 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27]
Number of open stations: 23

=================== for P=24
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x63944ca0
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 3332 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27]
Number of open stations: 22

=================== for P=25
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0x32ab1ba6
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 3332 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
Open stations: [0, 1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27]
Number of open stations: 23

=================== for P=26
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xaedb8953
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 3332 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
Open stations: [0, 1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27]
Number of open stations: 23

=================== for P=27
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xa6b75529
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 3332 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
Open stations: [0, 1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27]
Number of open stations: 23

=================== for P=28
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 3305 rows, 3332 columns and 6943 nonzeros
Model fingerprint: 0xe7946d32
Variable types: 0 continuous, 3332 integer (3332 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 3332 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 1797 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
Open stations: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]
Number of open stations: 28

Task: Repeat the whole process with another fishnet_points with different fishnet interval.

fishnet_points_mile = create_fishnet(5280)

Number of points in the fishnet: 330

fishnet_points_mile = fishnet_points_mile.reset_index(drop=True)
len(fishnet_points_mile)

128

I = 128
J = 28
a_i = [1] * I
D_ij = [[np.sqrt((fishnet_points_mile.geometry.x[i] - stations.geometry.x[j])**2 + 
                 (fishnet_points_mile.geometry.y[i] - stations.geometry.y[j])**2)
                  for j in range(J)] for i in range(I)]
N_i = [[j for j in range(J) if D_ij[i][j] <= S] for i in range(I)]

optimize_and_evaluate(demand_block=False)

=================== for P=3
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0xa5c1f76a
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+00, 3e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 106 rows and 116 columns
Presolve time: 0.00s
Presolved: 23 rows, 40 columns, 88 nonzeros
Found heuristic solution: objective 21.0000000
Variable types: 0 continuous, 40 integer (35 binary)

Root relaxation: objective 2.400000e+01, 25 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0      24.0000000   24.00000  0.00%     -    0s

Explored 1 nodes (25 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 24 21 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.400000000000e+01, best bound 2.400000000000e+01, gap 0.0000%
Open stations: [5, 14, 18]
Number of open stations: 3

=================== for P=4
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0xd591673c
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e+00, 4e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 106 rows and 115 columns
Presolve time: 0.00s
Presolved: 23 rows, 41 columns, 89 nonzeros
Found heuristic solution: objective 28.0000000
Variable types: 0 continuous, 41 integer (36 binary)

Root relaxation: objective 3.100000e+01, 22 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0      31.0000000   31.00000  0.00%     -    0s

Explored 1 nodes (22 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 31 28 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 3.100000000000e+01, best bound 3.100000000000e+01, gap 0.0000%
Open stations: [5, 14, 17, 18]
Number of open stations: 4

=================== for P=5
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0x4a009212
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e+00, 5e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 110 rows and 120 columns
Presolve time: 0.00s
Presolved: 19 rows, 36 columns, 79 nonzeros
Variable types: 0 continuous, 36 integer (34 binary)
Found heuristic solution: objective 31.0000000

Root relaxation: objective 3.700000e+01, 19 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0      37.0000000   37.00000  0.00%     -    0s

Explored 1 nodes (19 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 37 31 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 3.700000000000e+01, best bound 3.700000000000e+01, gap 0.0000%
Open stations: [5, 14, 15, 17, 18]
Number of open stations: 5

=================== for P=6
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0x55390191
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [6e+00, 6e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 110 rows and 120 columns
Presolve time: 0.00s
Presolved: 19 rows, 36 columns, 79 nonzeros
Variable types: 0 continuous, 36 integer (34 binary)
Found heuristic solution: objective 35.0000000

Root relaxation: objective 4.300000e+01, 17 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0      43.0000000   43.00000  0.00%     -    0s

Explored 1 nodes (17 simplex iterations) in 0.00 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 43 35 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 4.300000000000e+01, best bound 4.300000000000e+01, gap 0.0000%
Open stations: [2, 5, 13, 14, 17, 18]
Number of open stations: 6

=================== for P=7
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0x1929caf9
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [7e+00, 7e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 110 rows and 120 columns
Presolve time: 0.00s
Presolved: 19 rows, 36 columns, 79 nonzeros
Variable types: 0 continuous, 36 integer (34 binary)
Found heuristic solution: objective 41.0000000

Root relaxation: objective 4.800000e+01, 12 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0      48.0000000   48.00000  0.00%     -    0s

Explored 1 nodes (12 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 48 41 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 4.800000000000e+01, best bound 4.800000000000e+01, gap 0.0000%
Open stations: [2, 4, 6, 13, 14, 17, 18]
Number of open stations: 7

=================== for P=8
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0xa1907605
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [8e+00, 8e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 110 rows and 120 columns
Presolve time: 0.00s
Presolved: 19 rows, 36 columns, 79 nonzeros
Variable types: 0 continuous, 36 integer (34 binary)
Found heuristic solution: objective 51.0000000

Root relaxation: objective 5.200000e+01, 9 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0      52.0000000   52.00000  0.00%     -    0s

Explored 1 nodes (9 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 52 51 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 5.200000000000e+01, best bound 5.200000000000e+01, gap 0.0000%
Open stations: [2, 4, 6, 13, 14, 15, 17, 18]
Number of open stations: 8

=================== for P=9
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0xe9a18f38
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [9e+00, 9e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 110 rows and 120 columns
Presolve time: 0.00s
Presolved: 19 rows, 36 columns, 79 nonzeros
Variable types: 0 continuous, 36 integer (34 binary)
Found heuristic solution: objective 54.0000000

Root relaxation: objective 5.500000e+01, 9 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0      55.0000000   55.00000  0.00%     -    0s

Explored 1 nodes (9 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 55 54 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 5.500000000000e+01, best bound 5.500000000000e+01, gap 0.0000%
Open stations: [2, 4, 6, 11, 13, 14, 15, 17, 18]
Number of open stations: 9

=================== for P=10
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0xfeb442bc
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 110 rows and 120 columns
Presolve time: 0.00s
Presolved: 19 rows, 36 columns, 79 nonzeros
Variable types: 0 continuous, 36 integer (34 binary)
Found heuristic solution: objective 57.0000000

Root relaxation: objective 5.800000e+01, 8 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

*    0     0               0      58.0000000   58.00000  0.00%     -    0s

Explored 1 nodes (8 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 3: 58 57 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 5.800000000000e+01, best bound 5.800000000000e+01, gap 0.0000%
Open stations: [2, 4, 6, 9, 11, 13, 14, 15, 17, 18]
Number of open stations: 10

=================== for P=11
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0x5b1c1a19
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 110 rows and 120 columns
Presolve time: 0.00s
Presolved: 19 rows, 36 columns, 79 nonzeros
Variable types: 0 continuous, 36 integer (34 binary)
Found heuristic solution: objective 61.0000000

Root relaxation: cutoff, 4 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0     cutoff    0        61.00000   61.00000  0.00%     -    0s

Explored 1 nodes (4 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 2: 61 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 6.100000000000e+01, best bound 6.100000000000e+01, gap 0.0000%
Open stations: [2, 4, 6, 9, 11, 12, 13, 14, 15, 17, 18]
Number of open stations: 11

=================== for P=12
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0xa48f30b9
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 110 rows and 120 columns
Presolve time: 0.00s
Presolved: 19 rows, 36 columns, 79 nonzeros
Variable types: 0 continuous, 36 integer (34 binary)
Found heuristic solution: objective 63.0000000

Root relaxation: cutoff, 3 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0     cutoff    0        63.00000   63.00000  0.00%     -    0s

Explored 1 nodes (3 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 2: 63 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 6.300000000000e+01, best bound 6.300000000000e+01, gap 0.0000%
Open stations: [2, 4, 6, 9, 11, 12, 13, 14, 16, 17, 18, 25]
Number of open stations: 12

=================== for P=13
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0x4b6bcc9d
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 110 rows and 120 columns
Presolve time: 0.00s
Presolved: 19 rows, 36 columns, 79 nonzeros
Variable types: 0 continuous, 36 integer (34 binary)
Found heuristic solution: objective 64.0000000

Root relaxation: cutoff, 3 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0     cutoff    0        64.00000   64.00000  0.00%     -    0s

Explored 1 nodes (3 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 2: 64 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 6.400000000000e+01, best bound 6.400000000000e+01, gap 0.0000%
Open stations: [2, 4, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 25]
Number of open stations: 13

=================== for P=14
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0xe823640e
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 110 rows and 120 columns
Presolve time: 0.00s
Presolved: 19 rows, 36 columns, 79 nonzeros
Variable types: 0 continuous, 36 integer (34 binary)
Found heuristic solution: objective 65.0000000

Root relaxation: cutoff, 2 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0     cutoff    0        65.00000   65.00000  0.00%     -    0s

Explored 1 nodes (2 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 2: 65 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 6.500000000000e+01, best bound 6.500000000000e+01, gap 0.0000%
Open stations: [2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 25]
Number of open stations: 14

=================== for P=15
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0x60c4095b
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 110 rows and 120 columns
Presolve time: 0.00s
Presolved: 19 rows, 36 columns, 79 nonzeros
Variable types: 0 continuous, 36 integer (34 binary)
Found heuristic solution: objective 66.0000000

Root relaxation: cutoff, 3 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0     cutoff    0        66.00000   66.00000  0.00%     -    0s

Explored 1 nodes (3 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 2: 66 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 6.600000000000e+01, best bound 6.600000000000e+01, gap 0.0000%
Open stations: [2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 23, 25]
Number of open stations: 15

=================== for P=16
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0xcd911409
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 110 rows and 120 columns
Presolve time: 0.00s
Presolved: 19 rows, 36 columns, 79 nonzeros
Variable types: 0 continuous, 36 integer (34 binary)
Found heuristic solution: objective 67.0000000

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 2: 67 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 6.700000000000e+01, best bound 6.700000000000e+01, gap 0.0000%
Open stations: [2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 20, 23, 25]
Number of open stations: 16

=================== for P=17
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0x4379ff04
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 111 rows and 121 columns
Presolve time: 0.00s
Presolved: 18 rows, 35 columns, 74 nonzeros
Found heuristic solution: objective 68.0000000
Variable types: 0 continuous, 35 integer (33 binary)

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 20 (of 20 available processors)

Solution count 2: 68 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 6.800000000000e+01, best bound 6.800000000000e+01, gap 0.0000%
Open stations: [0, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 20, 23, 25]
Number of open stations: 17

=================== for P=18
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0x52a0f313
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 129 rows and 156 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 68 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 6.800000000000e+01, best bound 6.800000000000e+01, gap 0.0000%
Open stations: [0, 1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 20, 23, 25]
Number of open stations: 18

=================== for P=19
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0x5f486a89
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 129 rows and 156 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 68 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 6.800000000000e+01, best bound 6.800000000000e+01, gap 0.0000%
Open stations: [1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 20, 23, 25]
Number of open stations: 17

=================== for P=20
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0xb3e412df
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 129 rows and 156 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 68 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 6.800000000000e+01, best bound 6.800000000000e+01, gap 0.0000%
Open stations: [0, 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 20, 23, 25, 26]
Number of open stations: 20

=================== for P=21
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0x5b0cb681
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 129 rows and 156 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 68 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 6.800000000000e+01, best bound 6.800000000000e+01, gap 0.0000%
Open stations: [0, 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 20, 23, 25, 26]
Number of open stations: 20

=================== for P=22
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0x5809d8c3
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 129 rows and 156 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 68 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 6.800000000000e+01, best bound 6.800000000000e+01, gap 0.0000%
Open stations: [0, 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 20, 23, 25, 26]
Number of open stations: 20

=================== for P=23
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0x57d6422b
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 129 rows and 156 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 68 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 6.800000000000e+01, best bound 6.800000000000e+01, gap 0.0000%
Open stations: [0, 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 20, 23, 25, 26]
Number of open stations: 20

=================== for P=24
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0x458dd830
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 129 rows and 156 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 68 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 6.800000000000e+01, best bound 6.800000000000e+01, gap 0.0000%
Open stations: [0, 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 20, 23, 25, 26]
Number of open stations: 20

=================== for P=25
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0x144adec4
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 129 rows and 156 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 68 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 6.800000000000e+01, best bound 6.800000000000e+01, gap 0.0000%
Open stations: [0, 1, 2, 3, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 20, 23, 25, 26]
Number of open stations: 20

=================== for P=26
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0xe907070f
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 129 rows and 156 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 68 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 6.800000000000e+01, best bound 6.800000000000e+01, gap 0.0000%
Open stations: [0, 1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 20, 23, 25]
Number of open stations: 18

=================== for P=27
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0x72992fe0
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 129 rows and 156 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 68 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 6.800000000000e+01, best bound 6.800000000000e+01, gap 0.0000%
Open stations: [0, 1, 2, 4, 5, 6, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 25]
Number of open stations: 19

=================== for P=28
Gurobi Optimizer version 11.0.1 build v11.0.1rc0 (win64 - Windows 10.0 (19045.2))

CPU model: 12th Gen Intel(R) Core(TM) i7-12700, instruction set [SSE2|AVX|AVX2]
Thread count: 12 physical cores, 20 logical processors, using up to 20 threads

Optimize a model with 129 rows, 156 columns and 294 nonzeros
Model fingerprint: 0x47da8164
Variable types: 0 continuous, 156 integer (156 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 129 rows and 156 columns
Presolve time: 0.01s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)
Thread count was 1 (of 20 available processors)

Solution count 2: 68 -0 

Optimal solution found (tolerance 1.00e-04)
Best objective 6.800000000000e+01, best bound 6.800000000000e+01, gap 0.0000%
Open stations: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]
Number of open stations: 28

Question 10: Compare the Scatter plots out of Blocks, 0.2 mile fishnet points, and another fishnet points with interval of your choice. Discuss the insights you can get. ( 5 pts )

In Lab 2, we discovered that different Coverage Distance Standard can impact the coverage analysis result.
In Lab 4, we can discover how different demand representation makes difference.
Share your insights about

• provide three scatter plots ( 3 pts )
• how SBC_FD is currently doing with existing stations in terms of coverage ( 1 pt )
• how demand representation impacts the coverage analysis ( 1 pt )

TIP: you can copy and paste your screenshot into markdown cells

PUT your answer HERE

Coverage by Census blocks Coverage by .2 mile fishnet

Coverage by 1 mile fishnet

Currently Santa Barbara has too many stations. The could get a similer level of coverage with a mere 15 stations. Or fewer depending on the level of coverage than is needed. By variaing the size of the fishnets you run into a sort of MAU problem where the gridded nature of the cells make for a poor representation of the actual populaiton, as they tend to be clustered into a small area. Thus it is better to just stick to cencus blocks that are smaller when they encounter the areas with a higher population density.